Decomposition of the mean friction drag in zero-pressure-gradient turbulent boundary layers

The ability to understand and predict mean friction drag generation in wall-bounded turbulence is highly desirable in many engineering applications. In this paper, we decompose the mean friction drag in incompressible (250 ≤ Reτ ≤ 1270) and compressible (M = 2.0 and 250 ≤ Reτ ≤ 1110) zero-pressure-gradient turbulent boundary layers (TBLs) into three physics-informed contributions, by using the identity of Renard and Deck ["A theoretical decomposition of mean skin friction generation into physical phenomena across the boundary layer," J. Fluid Mech. 790, 339-367 (2016)] and its compressible-flow extension [Li et al., "Decomposition of the mean skin-friction drag in compressible turbulent channel flows," J. Fluid Mech. 875, 101-123 (2019)], respectively. The Reynolds number effects and scaling of each contributing term are investigated. Proportionality of the viscous and logarithmic increase with Reτ of the turbulent one when scaled by Cf3/2 are found, with different scaling coefficients in incompressible and compressible TBLs, owing to variation in the thermodynamic properties in the compressible cases. On use of compressibility transformations to account for variation in the thermodynamic properties in the wall-normal direction, the terms contributing to friction in compressible TBLs are found to reduce to those in the incompressible limit, with good accuracy. At M = 2.0, deviations from universality are mainly confined to the near-wall region, say y+ < 30, and account for approximately 16% of the generated friction.